We have to prove that tan(x + pi/4) = (cos x + sin x)/(cos x - sin x)

We know that tan (a + b) = [tan a + tan b]/(1 - tan a * tan b)

tan(x + pi/4)

=> (tan x + tan pi/4) / (1 - tan...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

We have to prove that tan(x + pi/4) = (cos x + sin x)/(cos x - sin x)

We know that tan (a + b) = [tan a + tan b]/(1 - tan a * tan b)

tan(x + pi/4)

=> (tan x + tan pi/4) / (1 - tan x * tan pi/4)

tan pi/4 = 1

=> (tan x + 1) / ( 1 - tan x)

=> [(sin x / cos x) + 1]/[1 - (sin x / cos x)]

=> [(sin x + cos x)/cos x]/ [(cos x - sin x)/cos x]

=> (sin x + cos x)/ (cos x - sin x)

**This proves that tan(x + pi/4)= (cos x + sin x)/(cos x - sin x)**